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Power Method for Eigenvalues | Numerical Methods Lab
Numerical Methods - Power Method

Lab 3: Power Method for Eigenvalue Problems

Lab 3: Power Method for Finding Dominant Eigenvalue and Eigenvector

Experiment Information

Experiment: Power Method for finding largest eigenvalue and eigenvector

Course Code: Numerical Methods

Description: Complete lab report covering theory, algorithm, Python implementation and analysis of Power Method

Prepared by: Important Notes Team

Complete Lab Report PDF

1. Theory of Power Method

1.1 Mathematical derivation of iterative method

1.2 Convergence criteria and rate

1.3 Dominant eigenvalue concept

2. Algorithm

2.1 Step-by-step procedure

2.2 Normalization process

2.3 Stopping criteria

3. Implementation

3.1 Python code with numpy

3.2 Input/output specifications

3.3 Handling non-convergent cases

4. Observations

4.1 Data recording table

4.2 Sample calculations

4.3 Convergence behavior

5. Results

5.1 Eigenvalue approximation

5.2 Eigenvector approximation

5.3 Error analysis

6. Discussion

6.1 Advantages and limitations

6.2 Comparison with other methods

6.3 Applications in engineering problems

Digitized lab report prepared by Important Notes Team

Python Implementation of Power Method

power_method.py
import numpy as np

A = np.array([[3,2,3],
              [2, 4,6],
              [-3,-6,-15]])
n=len(A)
X = np.ones(n)
p=3
tol=0.5*10**(-p)
count=0
while True:
    count+=1
    if count>100:
        raise Exception("Unable to find Eigenvalue.")
    Z=np.dot(A,X)
    L=np.sqrt(np.dot(Z,Z))
    Y=Z/L
    if np.dot(X,Y) < 0.0:
        L=-L
        Y=-Y
    print(L,Y)
    D=np.abs(Y-X)
    err=np.max(D)
    X=Y.copy()
    if err < tol:
        break

print("Largest Eigenvalue:",L)
print("Corresponding Eigenvector:",Y)
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